gwr-inversion 1.0.1

Gaver-Wynn-Rho Algorithm

This is a Python reproduction of the Mathematica package that provides the GWR function, NumericalLaplaceInversion.m.

https://library.wolfram.com/infocenter/MathSource/4738/

This package provides only one function: gwr. The function calculates the value of the inverse of a Laplace transform at a specified time value, Sequence of time values, or numpy array of time values.

The Laplace transform should be provided as a function that uses the mpmath library for a scalar value of the Laplace parameter. The math library and numpy functions do not support multiprecision math and will return invalid results if they are used.

Simple Example

>>> import math
>>> from gwr_inversion import gwr
>>> from mpmath import mp

>>> def lap_ln_fn(s: float):
...     # log function
...     return -mp.log(s) / s - 0.577216 / s

>>> gwr(lap_log_fn, time=5.0, M=32)
    mpf('1.6094375773356333')

>>> math.log(5.0)
1.6094379124341003

See the notebooks in test\ for other use examples.

The method is described in: Valkó, P.P., and Abate J. 2002. Comparison of Sequence Accelerators for the Gaver Method of Numerical Laplace Transform Inversion. Computers and Mathematics with Application 48 (3): 629–636. https://doi.org/10.1016/j.camwa.2002.10.017.

More information on multi-precision inversion can be found in: Valkó, P.P.and Vajda, S. 2002. Inversion of Noise-Free Laplace Transforms: Towards a Standardized Set of Test Problems. Inverse Problems in Engineering 10 (5): 467-483. https://doi.org/10.1080/10682760290004294.